Ok so I fixed all that by install yarn/rollup manually.
The updates were successful and I am now able to run the following:
$bench switch-to-branch version-12 --upgrade
$ bench update --patch
But the when I try to access the site, it throws the following errors:
404 Not Found : assets/css/frappe-web-b4.css
404 Not Found : /assets/js/bootstrap-4-web.min.js
And an error on the console:
Uncaught TypeError: $(...).dropdown is not a function
at HTMLDocument.<anonymous> (frappe-web.min.js:1)
at HTMLDocument.dispatch (jquery.min.js:3)
at HTMLDocument.r.handle (jquery.min.js:3)
at Object.trigger (jquery.min.js:4)
at HTMLDocument.<anonymous> (jquery.min.js:4)
at Function.each (jquery.min.js:2)
at n.fn.init.each (jquery.min.js:2)
at n.fn.init.trigger (jquery.min.js:4)
at HTMLDocument.<anonymous> (frappe-web.min.js:1)
at i (jquery.min.js:2)
Thanks for your help.